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Simplifying 3x2 + -12x + 21 = 47 Reorder the terms: 21 + -12x + 3x2 = 47 Solving 21 + -12x + 3x2 = 47 Solving for variable 'x'. Reorder the terms: 21 + -47 + -12x + 3x2 = 47 + -47 Combine like terms: 21 + -47 = -26 -26 + -12x + 3x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -26 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -4x + 8.666666667 + x2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -4x + x2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + 8.666666667 -4x + x2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -4x + x2 = 8.666666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 8.666666667 + 4 Reorder the terms: 4 + -4x + x2 = 8.666666667 + 4 Combine like terms: 8.666666667 + 4 = 12.666666667 4 + -4x + x2 = 12.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 12.666666667 Calculate the square root of the right side: 3.559026084 Break this problem into two subproblems by setting (x + -2) equal to 3.559026084 and -3.559026084.Subproblem 1
x + -2 = 3.559026084 Simplifying x + -2 = 3.559026084 Reorder the terms: -2 + x = 3.559026084 Solving -2 + x = 3.559026084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.559026084 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.559026084 + 2 x = 3.559026084 + 2 Combine like terms: 3.559026084 + 2 = 5.559026084 x = 5.559026084 Simplifying x = 5.559026084Subproblem 2
x + -2 = -3.559026084 Simplifying x + -2 = -3.559026084 Reorder the terms: -2 + x = -3.559026084 Solving -2 + x = -3.559026084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.559026084 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.559026084 + 2 x = -3.559026084 + 2 Combine like terms: -3.559026084 + 2 = -1.559026084 x = -1.559026084 Simplifying x = -1.559026084Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.559026084, -1.559026084}
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